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Monday, March 31, 2008

In a recent post, I described a market timing experiment where a market timer decides each month whether to own the S&P 500 or to hold all cash. The result was that the market timer had to guess right 60% of the time from December 1990 to March 2008 to keep pace with an investor who simply bought and held through the whole time period.

That experiment assumed that the investor was using a tax-sheltered account, as the Canadian Capitalist observed in his comment on that post. What happens if you have to pay taxes on the interest, dividends, and capital gains? I ran the experiment again, this time taking into account taxes. To give the market timer as much help as possible, I assumed that the buy-and-hold investor sells everything at the end of the complete time period and pays capital gains taxes.

Tax rates vary from one jurisdiction to the next. For this experiment, I assumed a tax rate of 40% on interest income and 20% on dividends and capital gains.

I assume that the market timer has some fixed probability of making the right choice each month. Once again, I calculated the market timer’s compound yearly return for various probabilities of making the better choice. Here are the results:

Comparing these results to the tax-free results from the earlier post, we see that taxes hurt the market timer more than the buy and hold investor. Now the market timer has to be right 63% of the time (up from 60% in the tax-free case) to break even with the buy and hold investor.

It may not seem difficult to be right 63% of the time, but every time you choose to jump in or out of stocks, you’ll need to trade with someone who gets it wrong 63% of the time. The truth is that most of the time owning stocks is the right thing to do, and selling is the wrong thing to do. This makes it very difficult to guess the right time to be out of the market with high probability.

If you are investing in an account that isn’t tax sheltered, you have even more reason to avoid market timing.

Friday, March 28, 2008

Government intervention into the US housing crisis has become an issue in the ongoing presidential race. McCain, Clinton, and Obama have each made statements about how the crisis should be handled. I find that my opinion on this matter shifts depending on who I focus on. Let me go through some hypothetical players so that I can show you what I mean.

Case 1: Irresponsible Homeowner

Carl saw his friends making money from rising house prices and decided to buy a condo to get in on the action. He chose a condo selling for $280,000, but he couldn’t really afford it on his modest income. In an obviously shady arrangement at the height of mortgage excesses, he managed to get a mortgage for $300,000 with only half-size payments for the first year.

Carl knew he couldn’t afford the higher payments after the first year. His plan was to profit from the increased value of his condo in a year by either selling it or renegotiating his mortgage based on the new condo value.

Things haven’t worked out very well for Carl. He can only get $150,000 for his condo, but he owes $310,000 on his mortgage and he can’t afford the payments. Carl is going to lose everything.

With Carl in mind, it’s hard to see why the government should do anything. He took a wild chance based on greed and lost. He deserves what he gets. Helping him would be a waste of public money.

Case 2: Responsible Homeowner

Judy and her husband saved for years and finally bought a home two years before the housing boom peaked. The price was a bit of a stretch, but they could handle it on their two incomes. They got a standard mortgage from a responsible lender. A year later, Judy’s husband lost his job. But, they have just barely managed to make the mortgage payments anyway.

Judy would be able to continue this way if the mortgage payments stayed the same, but if the crisis keeps getting worse, lenders may start to raise interest rates causing Judy to lose her home.

It is easy to see why it makes sense for the government to intervene to make sure that people like Judy stay afloat. If too many people like Judy get forced into bankruptcy, it would cause huge social problems.

Case 3: Reckless Lender

The people working for WildCapital knew a good thing when they saw it. They could make huge commissions selling mortgages to people who couldn’t really afford them. And as long as the housing prices kept rising, their reckless lending wouldn’t lead to foreclosures and the party could continue.

Now that the bubble has burst, WildCapital’s customers have given up their homes, and WildCapital is left owning houses whose total value doesn’t come close to covering their debts. WildCapital is about to go bankrupt.

Good riddance. Bad companies should go bankrupt. A huge part of the ongoing success of the US economy has been that good companies thrive and bad ones disappear. WildCapital should not be bailed out by the government.

Case 4: Responsible Lender

SteadyCapital refused to lower its lending standards through the housing bubble. As a result, they lost a lot of business to companies like WildCapital. What’s worse, SteadyCapital is at risk now if the crisis spreads to its customers like Judy.

It’s clear that the government should step in to protect customers like Judy and companies like SteadyCapital. But, the assistance should not be so great that it saves WildCapital. Otherwise, the government is essentially subsidizing WildCapital so that it can continue to steal business away from SteadyCapital.

What to do?

One hard part in all this is to figure out which borrowers and lenders are reckless and which are responsible. Another hard part is to figure out what sort of government action will have the desired effects.

Throughout all the political discussions from the three presidential hopefuls, I can’t tell which course of action is best. I welcome any comments that might help with figuring this out.

Thursday, March 27, 2008

All available evidence and logic tell us that the vast majority of investors can’t beat the market by market timing. This applies to professional money managers as well. I tried a little experiment to see how accurate a market timer’s predictions would have to be to succeed at beating the market.

Market timing refers to the practice of jumping in and out of the stock market in an attempt to avoid market declines.

The Experiment

Suppose that a market timer decides at the beginning of each month whether to have all of his money in the S&P 500 stocks or all of it in cash. His goal is to avoid being in stocks during the months where stocks perform worse than cash.

Each month the market timer has a certain probability of guessing right. If he just tosses a coin, this probability is 50%. The question is how high this probability has to be for the market timer to beat the strategy of just buying and holding through thick and thin.

I gathered data on the S&P 500 from December 1990 to March 2008 and ran some simulations. For each fixed probability of the market timer guessing right each month, I ran 10 million Monte Carlo simulations and averaged out the results.

To account for commissions, costs due to stock spreads, and interest on cash, I assumed that the net return of interest minus costs averaged 3% per year while the market timer has his money out of stocks.

The Results

A buy and hold investor over this period of time would have received an average compound return of 11.0% per year. From the results chart, we see that the market timer has to be right 60% of the time just to break even with the investor who buys and holds.

If the market timer is right only 50% of the time, he will underperform the buy and hold strategy by 4.2% per year, on average. This is a huge penalty for just guessing.

Over the full period, an initial investment of $100,000 grew to $606,000 by buying and holding. A market timer who tosses a coin each month will have a median outcome of only $312,000! This shows that our market timer missed many months where stocks rose significantly.

It seems to be human nature to be tempted to believe that we can do better than buying and holding by anticipating market declines. The next time you are tempted to try market timing, remember that you have to be right 60% of the time (and the people you trade against have to be wrong 60% of the time) just for you to break even. Do you really believe that you are that much better than all the other market timers?

Wednesday, March 26, 2008

People have a lot of tendencies that serve them well in many aspects of their lives, but can be harmful when it comes to investing in stocks. One of these tendencies is to prefer the familiar over the unfamiliar.

I saw this during the high-tech bubble when ordinary people with minimal investing experience suddenly had stock options worth more than their houses. For some reason, these people found it difficult to cash out even though the stock options represented 80% or more of their net worth.

I used to try a little mental exercise with these people. I would say “imagine that your options have been cashed out and the money is sitting in your bank account. Would you use it all to buy stock in a high-tech company at soaring prices?”

The usual answer was something like “No way! That would be a ridiculously risky thing to do.” But, to my knowledge, only one person who tried this mental exercise with me was persuaded to cash out most of his options. Most people continued to hold their options until well after the bubble burst.

For some reason, people felt more comfortable with the familiar situation where they continued to hold their options. Cashing out felt risky to them, even though cashing out actually would have dramatically lowered their financial risk.

A Simple Rule

Whenever you are trying to decide whether to sell some asset, you should ask yourself “if I had the money, would I buy this asset right now?” If the answer is no, then you should probably sell. This approach is particularly important when one asset has grown to dominate your portfolio.

Some Caveats

Of course, there are some caveats with this method of deciding when to sell. If you decide that a stock is worth owning at $30, and you buy it today for $29.99 per share, it makes no sense to sell it tomorrow for $30.01 per share.

You need to take into account trading commissions, the cost of spreads, and taxes. Based on these considerations, you may decide that a stock is worth buying below $30, should be sold above $60, and just held for any price in between.

This doesn’t necessarily mean that you should automatically sell the stock if it hits $60 say 2 years from now. If the company’s fortunes have improved dramatically, you may change your holding range to $50-$100. Even if the stock stays at $30, you may sell if the company’s business goes downhill, and your range changes to $10-$20.

Where do these ranges come from?

These ranges come from a fundamental analysis of the company’s business and future prospects. If you don’t know how to do this, then you should consider sticking to an indexing strategy for the stock portion of your portfolio rather than buying individual stocks.

Tuesday, March 25, 2008

Bloomberg reports that mutual funds are selling stocks and hoarding cash. Of course, this would have been a better strategy when stocks were at a peak, rather than after they have dropped. This is definitely not a case of better late than never.

When it comes to selling stocks in anticipation of dropping prices, I take the approach of better never than late. I just stay invested in stocks through the ups and downs because I don’t believe that I can predict the future direction of the market. It always seems easy to look back and think that what happened was inevitable, but it’s never so easy when you look forward.

Mutual funds have a history of selling stocks at market lows and buying in at market highs. We can see this by tracking their cash levels. At market lows mutual funds tend to have high cash levels, and at market highs they tend to have low cash levels according to Larry Swedroe in his book “Rational Investing in Irrational Times.”

So, it seems that the professional money managers running mutual funds are no better than I am at predicting the future of the stock market.

I feel confident in predicting that the current pain in the stock market will end sometime, but I have no idea when. Many individual investors will continue to sell their stocks and “wait until things get better.” This strategy will work for some of them. However, many of these investors will get it wrong and will miss the rebound in stock prices. So, I’m just going to sit tight.

Monday, March 24, 2008

When we save for retirement, we tend to focus on that magical day when we will stop working. However, you won’t need to withdraw your entire retirement savings all at once on that day. For the most part, you’ll just need a certain amount per month plus the odd larger amount for things like a car, boat, or skydiving gear.

Your retirement could easily last for more than 20 years. So, you’ll have to continue making decisions about how to invest your savings after you’ve retired.

Most people (including me) believe that it makes sense to invest more conservatively as you get older. This usually means increasing the amount of money you invest in bonds and cash rather than stocks. In his book “Rational Investing in Irrational Times”, Larry Swedroe offers the following guidelines for percentage of money in stocks vs. how long it will be until you need the money:

I discussed how reasonable this advice is here and here. But, let’s just take this table at face value for now.

It is easy to misinterpret this table. It doesn’t refer to the number of years before retirement. It refers to the number of years until you’ll need the money.

Think of splitting your retirement savings into many separate pots, one for each month of your retirement. (This is just a mental exercise – you don’t actually have to split your money up.) On the day you retire, your first 3 years of monthly withdrawals will not be in stocks at all. However, your monthly withdrawals planned for 20 years from now will still be 100% in stocks.

Let’s say you are planning a 25-year retirement. That’s 300 monthly withdrawals. At any given time each one of these monthly amounts has its own percentage of allocation to stocks. It would be nice to blend these percentages together to get the overall percentage allocated to stocks.

I worked out the stock allocation based on the following assumptions:

1. You’ll withdraw the money steadily each year of retirement in amounts that grow with inflation.2. Your stocks will grow at an average compound rate of 6% above inflation.3. Your fixed income investments will average 2% above inflation.

I rounded the results to the nearest 10% partly because exact figures are pointless and partly to shrink the size of the resulting table. Here are the results:

Before Retirement:14+ years before: 100% in stocks8-13 years before: 90% in stocks6-7 years before: 80% in stocks4-5 years before: 70% in stocks1-3 years before: 60% in stocks

After Retirement:0-4 years after: 50% in stocks5-10 years after: 40% in stocks11-13 years after: 30% in stocks14-16 years after: 20% in stocks17-18 years after: 10% in stocks19+ years after: 0% in stocks

So, it turns out that following Swedroe’s advice, we still have half our money invested in stocks for the first few years after retirement. The assumptions that went into these calculations may not apply to everyone, but for almost any set of reasonable assumptions, retirees still need to allocate some of their savings to stocks.

Friday, March 21, 2008

Insider trading is buying or selling a company’s stock when you have important inside information about the company that has not been made public. We tend to think of insider trading as being illegal, but that is an oversimplification.

The top executives of a company almost always have inside information. If insider trading were illegal, then these executives could never trade their own stock. In the US, insiders are allowed to create prearranged trading plans, called 10b5-1 plans, for trading stock.

The idea is that the executives can set out a plan to commit to trading stock at particular prices or at particular times. This way, the stock trades will happen automatically when the time comes, and the executive is protected from accusations of insider trading.

Insiders beat the average

But the insiders still seem to outperform other traders significantly. Business Week reported that “Alan D. Jagolinzer, an assistant professor at Stanford University Graduate School of Business, recently completed a study of roughly 117,000 trades in 10b5-1 plans by 3,426 executives at 1,241 companies. He found that trades inside the plans beat the market by 6% over six months. By contrast, executives at the same firms who traded without the benefit of plans beat the market by only 1.9%.”

It is possible that these executives had great insight into the future performance of their companies at the time they set up the prearranged trading plans. But there are other possibilities as well.

Tinkering with the trading plans

According to Business Week, “despite the 'prearranged' nature of the trading plans, executives have enormous flexibility to start, stop, restart, and amend them at will. Some use the plans to trade just once; others use overlapping plans.”

So, it appears that in many cases these trading plans are being abused to allow executives to trade at will in their company’s stock.

The next time you think that maybe you could make a fortune day trading, remember that in addition to trading against other day traders and paying commissions frequently, you may be trading against a company executive who knows what is likely to happen much better than you do.

Thursday, March 20, 2008

The Dividend Guy challenged other bloggers to post their top 3 investing mistakes. Here is my contribution.

1. Putting my first savings into fixed income investments

I was young and nervous because I owed $85,000 on my first mortgage. My mortgage permitted doubling monthly payments, and my wife and I were taking advantage of this feature every month; I wanted the mortgage GONE. This didn’t leave much for retirement savings, but we did manage to save some money each year.

Unfortunately, I knew very little about the stock market at that time, and we put all of our savings into fixed income investments at our bank. We continued this way for several years giving up the gains available in the stock market. This was a big mistake.

2. Buying actively-managed high-cost mutual funds

My first tentative steps into the stock market were through mutual funds. I worked with a few different financial advisors who turned out to be little more than mutual fund salespeople. It took me quite a while to figure out that I was paying exorbitant fees to own these funds.

Sadly, like most mutual funds, my funds underperformed the index despite the assurances from my financial advisors that I owned some of the best mutual funds available.

3. Owning too much of my employer’s stock

I owned stock in my employer during the high-tech bubble. Fortunately, I sold most of it before the bubble burst, but it would have been a lot smarter to have kept the value of my employer’s stock below some percentage of my total portfolio, such as 20%. If the bubble had burst earlier, I could have lost most of my savings.

Situations like this are often tragic. Take Enron for example. Many employees had the bulk of their savings in Enron stock. They lost most of their money along with their jobs all at the same time. This was a very painful lesson for these people.

Larry Swedroe describes front running in his excellent book “Rational Investing in Irrational Times.” A fund family starts up a new fund hoping to report good returns and attract a flood of investors. They begin by choosing some stock that has low trading volumes so that a modest size purchase will drive its price up sharply.

The fund family then purchases a block of shares for the new fund. Then they purchase a larger block of shares for one or more of their large established funds. This will drive the price of the shares up and artificially inflate to apparent returns of the new fund.

Done correctly, the number of shares purchased for the established funds isn’t enough to make much of a difference to their returns. But, the new fund’s returns will look great and with a little advertising, new investors should flood in.

Of course, the reported returns don’t reflect any particular talent of the new fund’s manager. After the new fund swells, it isn’t any more likely than any other fund to do well. Investor’s should view the reported returns of any new fund sceptically.

Tuesday, March 18, 2008

Well, this is it. It’s obvious now that the stock market will never come back, and that we’re dropping into a permanent recession. Unfortunately, not everyone believes this yet. You see, things can’t start improving until everyone believes that they will never improve.

It’s time to head out and buy supplies for your bunker, unless you still have some left over from when the world was going to end in the year 2000. Whatever you do, don’t say anything optimistic about the future of the economy.

Remember, it’s not what happens in a year or more that matters, it’s the anticipated carnage tomorrow that we need to focus on. How can we handle these enormous problems?

I proceed by recognizing that I don’t know how to predict when the stock market will go up or down. So, I don’t try to buy or sell in anticipation of market moves. To deal with today’s low stock prices, I have kept money I’ll need in the short term out of stocks. Now, I’ll hunker down and hope that things get better in a few years.

This approach is much more boring than selling stocks at low prices in a panic, missing the big rebound in stock prices, and buying back in at higher prices. But I’ll stick with the boring method of just waiting out market declines.

I’m not a fan of using leverage (borrowing money to invest), but it is curious that your odds of succeeding with leverage are much better now than they were when market prices were higher and climbing. This is true even though investor enthusiasm for leverage was probably much higher when stocks were more expensive.

Stock market declines are inevitable. Everyone needs a realistic plan for dealing with them. If you can’t stay calm, then there may be something wrong with your plan.

Monday, March 17, 2008

I couldn’t agree more with Larry MacDonald’s take on Eliot Spitzer’s troubles (the web page with this article has disappeared since the time of writing).

On a personal level, Spitzer’s choice to make use of a prostitute is a serious matter for him and his family. He deserves some pain for his actions.

However, a much more serious matter for anyone who invests in the US is his effort to clean up the investment industry. The investment industry has legal responsibilities to act in the best interests of investors when handling their money. However, it is fair to say that much of the industry focuses on working around these laws to acquire as much investor money for themselves as possible.

Spitzer was heavily criticized for his attempts to clean up the investment industry, but these criticisms came mainly from those making money by taking it from investors. Chuck Jaffe has an interesting article discussing some of Spitzer’s efforts.

Spitzer’s personal failings are a serious matter for his family, but are trivial compared to the billions of dollars lost by investors each year. Individual investors need more politicians willing to fight against corruption in the investment industry.

Friday, March 14, 2008

Most commentators advise investors to shift money from equities to fixed income as they age, and this makes sense. We may disagree on the exact asset allocation percentages and exactly how soon before (or after) retirement to start lightening up on equities, but it seems clear enough that the average 40-year old should have more in equities than the average 80-year old.

However, there is a body of academic work that argues that investors should maintain a constant asset allocation regardless of their age. This work is based on what is known as constant relative-risk aversion (CRRA). I’ll show the problems with CRRA in an example below.

One consequence of the CRRA assumption is that the optimal asset allocation percentages remain constant regardless of the length of the investor’s investment horizon. Paul A. Samuelson advocates this view in his keynote address to “The Future of Life-Cycle Saving and Investing” conference.

I first heard of this conference and the corresponding free online book from this post over at Canadian Financial DIY. Despite the fact that I disagree with one part of this online book, as a whole it is very interesting and makes you think.

To show the problem with CRRA, I’ll consider a case where it gives silly results. To do this, I’ll have to pick a particular constant level of risk aversion. Morningstar uses the CRRA assumption in their star rating system for mutual funds. I’ll base my analysis on the risk aversion level chosen by Morningstar.

A Fun Example

A beer company decides to promote their new brand of beer sold in cases of 24 by roaming around to different bars giving away $24 to people who are drinking the new brand. The prize crew enters a bar and descends on a table where two friends, average Avery and rich Richard, are sitting drinking the new brand of beer.

As both men accept their $24 prizes, Avery is thrilled, but Richard is only mildly pleased. Avery comments “I guess a rich guy like you doesn’t get very excited by a lousy $24. How much bigger would your prize have to be to make you as excited as I am?”

The answer to this question depends on how much money Avery and Richard have. Suppose that Avery’s net worth is $120,000, and Richard’s is $6 million. According to the CRRA assumption, to make Richard as excited as Avery, his prize would have to be $340 million! This is obviously ridiculous.

Just for fun, let’s make some seemingly inconsequential changes. Each man calculates his net worth more accurately, and Avery’s comes out $20 higher than he first thought, and Richard’s comes out $2400.10 higher than he first thought. Now, the CRRA says that Richard’s prize must be $11 trillion!

You may find it hard to believe that CRRA could get these answers so horribly wrong, but that is what the math says. In fact, if Avery’s prize were $25, then according to CRRA there would be no amount you could give to Richard to make him as happy as Avery.

Is This a Fair Test? Yes, it is.

Most theories are based on approximations and simplifying assumptions. These theories can be shown to be wrong in extreme or unimportant cases. However, my example is directly relevant to long-term investing. CRRA gives answers that are close for small risks. But, for the large dollar amounts involved in long-term investing, CRRA gives ridiculous answers.

Matthew Rabin has an interesting paper where he discusses the problems of extrapolating from people’s attitudes about small risks to making decisions about large risks.

In truth, CRRA is more of a mathematical convenience than a valid theory. With CRRA, how much money you have and how much money you want to have aren’t relevant when deciding on your asset allocation. Without CRRA, Morningstar would not be able to give star ratings for mutual funds without knowing your net worth and your future needs for money.

So, if anyone tries to tell you to maintain the same asset allocation for your whole life, remember that this advice is based on a faulty theory.

Thursday, March 13, 2008

Many investors seem unaware of the fees they pay to own their mutual funds. Disclosure rules are intended to prevent this sort of problem, but they don’t seem to be effective enough. In an earlier post, I discussed the possibility of including fee summaries on financial statements.

An even better time to properly disclose fees is when you first start working with a financial advisor. Suppose that you meet with a financial advisor and agree to invest with her. She seems like a great person, and her investment advice seems sensible as far as you can tell. Then she hands you the following disclosure statement:

Gulp. Surely these can’t be right. Will you really pay this much? Yes, you will. These numbers were calculated based on the fees charged by three popular mutual funds offered in Canada. The bond fund has no load, the stock fund has a deferred sales charge, and the international stock fund has a front-end load. The dollar amounts assume a 4% per year return in the bond fund and an 8% per year return in the stock funds.

This type of disclosure would be a real eye-opener for investors and would make it harder for financial advisors to hide fees. It might also encourage more competition on fees among mutual funds.

Wednesday, March 12, 2008

All mutual funds have a management expense ratio (MER) that covers the costs of running the fund. In addition to the MER, some mutual funds charge “loads”. Loads are fees paid either when you buy into a fund (front-end load) or sell out of a fund (back-end load). Back-end loads are also called deferred sales charges.

The purpose of a front-end load is simple enough. The financial advisor who sells you a mutual fund is paid out of front-end loads. But what about funds that have deferred sales charges? Does the financial advisor have to wait until you sell to get his money?

Things look even worse for the financial advisor when the deferred sales charges are “contingent”. This means that the sales charge declines over time. In a typical arrangement, if you sell in the first year, you get charged 5% of your initial investment, but only 4% if you sell in the second year, and so on until it drops to zero in the sixth year.

Does this mean that if you hold on for more than 5 years your financial advisor doesn’t get paid? No, it doesn’t. The financial advisor gets paid up front regardless of whether the load is up front or deferred. This is easier to understand if you look at deferred charges another way.

Suppose that you invest $50,000 into a mutual fund with a 2% MER with a declining deferred sales charge starting at 5%. A better way to think of this is that you pay $2500 up front and get a $500 rebate on the MER for the first 5 years. After the fifth year, you pay the normal MER.

With this view, the only difference between front and back-end loads is the MER rebate. It is easy to see now how the financial advisor gets paid up front either way.

Don’t be fooled by deferred sales charges. They are effectively large up-front fees that aren’t much different from front-end loads.

Tuesday, March 11, 2008

Before reading her latest book “Women & Money,” I didn’t know much about Suze Orman other than the fact that she is a TV personality who talks about money. I wasn’t expecting much from her book but was pleasantly surprised.

The book is billed as “for women only,” but this mostly applies to the first 55 pages devoted to motivating women to read (and act on) the rest of the book. If you have thoughts on how useful these 55 pages are, I’d be interested in hearing them; they didn’t really apply to me.

The actual financial advice starts in Chapter 6, and most of it applies to men as well. The section on retirement investing (page 115) is particularly good. Much of the detailed advice is intended for Americans, but the broad advice is useful for Canadians as well.

Orman recommends that until you are a few years away from retirement, 100% of your retirement money should be invested in stock index funds. She prefers low-cost index exchange-traded funds (ETFs), but considers low-cost index mutual funds to be acceptable as well.

It was refreshing to read something other than the standard advice to allocate your investments on some percentage basis to each of cash, bonds, and stocks. Apart from emergency cash reserves, and short-term bonds for money you will need to spend in the next 3 or so years, I have never found a good reason to hold cash or bonds for the long term.

Monday, March 10, 2008

In an earlier post I was looking at what fraction of your portfolio should be in stocks. I also listed Larry Swedroe’s table of time horizon vs. stock percentage from his book “Rational Investing in Irrational Times”.

His table basically says to put everything in stocks if you won’t need the money for 20 or more years. The stock percentage then drops steadily to zero when you are three years from needing the money. I’ve been looking for some justification for this advice.

The answer comes from considering the utility of money. The basic idea of utility is that the wealthier you are, the less an additional dollar is worth to you.

An Example

Suppose that if you invested your entire portfolio in risk-free investments, you would have $1 million when you retire. A game show host then makes you the following offer. You can just take the $1 million or you can toss a coin to get either $800,000 or $2 million. Would you take the sure $1 million or would you take the chance?

What I really want to know is how much lower (or higher) than $800,000 you would be willing to go before the two options looked equally attractive to you. This gives an idea of your level of risk aversion.

Risk Aversion

I developed a model of risk aversion based on the idea that underperforming the risk-free return causes pain, and the answer to the coin-flip question determines the amount of pain. More details on this model are at the end of this post.

In applying this model, I assumed that your pain level is always relative to what you could get with risk-free investments. So, if your investments perform extremely well for a few years, and risk-free investing the rest of the way would give you $1.5 million, you would consider it painful to underperform $1.5 million even though a few years earlier the pain was relative to the $1 million level.

Similarly, if your investments perform poorly for a few years, and risk-free investing would give you $750,000, you would consider it painful to underperform $750,000.

The Results

I did the computations assuming the following. You consider a coin flip between $800,000 and $2 million to be equally desirable as a sure $1 million. Also, you consider a coin flip between $700,000 and $4 million to be equally desirable as a sure $1 million. This is a high degree of pain for underperformance. I also used the stock returns and volatility from a paper by John Norstad.

Here is the resulting table of time horizon vs. stock percentages. The percentages are rounded to the nearest 5% because any further precision is pointless.

Don’t get too attached to this table, though. The results are very sensitive to the answers to the coin-flip question. Consider the following two cases.

Case 1: You consider the coin flips ($900,000 or $2 million) and ($850,000 or $4 million) to be equally desirable as a sure $1 million. In this case, you would be less than half in stocks even 30 years from needing the money.

Case 2: You consider the coin flips ($700,000 or $2 million) and ($550,000 or $4 million) to be equally desirable as a sure $1 million. In this case, you would be 100% invested in stocks even during the last year before needing the money.

In conclusion, I doubt that there will ever be any single answer to the equity allocation question. I tend to lean toward staying fully invested in stocks until I’m about 3 years from needing the money, but I may change my mind if I find a convincing argument to take a different approach.

The Model (lots of math)

I came up with a series of points on a graph that reflected the pain of underperformance, and then found an equation to fit this curve. The challenge was to find an equation that made sense even in extreme cases, but also made the math easy enough to work with when applying the model.

Here are the parameters and the equation:

X – The final dollar amount after the returns on investments.T – A threshold dollar amount below which the investor starts to feel pain.a – A parameter for the incremental pain once underperformance is deep.b – A parameter for determining what is considered to be deep underperformance.P – Pain function.

P(X) = (X/T)^(a(1-(X/T)^b))

The idea here is that when optimizing expected compound returns, any return X that is below threshold T is changed to the smaller value X*P(X) to reflect the investor’s pain. I don’t know if anyone has used this particular pain function before.

The function P may not look very simple, but when we operate in the log domain it permits fairly easy integration when multiplied by the normal probability density function. All optimization is done in the log domain because we are optimizing compound returns while using the pain function. If we let p=ln(P), x=ln(X), and t=ln(T), then we get

p(x) = a(x-t)(1-e^(b(x-t))),

and if x is below the threshold t, we replace x with x+p(x). Note that p(x) is negative when x is less than t.

The parameters a and b were computed so that the function P(X) would match the coin-flip answers. For the table I listed above, these parameters were a=4.74 and b=2.64.

When I applied this model, the threshold of pain was always set at the risk-free return over the remaining years of investing. I began by finding the optimal stock percentage for the last year before the money is needed. Then I optimised the case where there are 2 years left to go knowing what would happen in the last year. I continued this for 40 years worth of results.

Friday, March 7, 2008

A strategy is said to be dominated if it is guaranteed to give the same or worse results than some other strategy. This term is usually used in game theory, but it can apply equally well to investing.

Most of the time when we have a choice between two alternatives, we don’t know for certain which choice will lead to a better outcome. Should you buy stocks or bonds? In a given year, stocks might give better returns or bonds might give better returns.

In some cases, the choice turns out to be clearer. Suppose that I offer you a bet: we’ll toss a coin, and the winner gets $100 from the loser. I see you hesitate, and I make a second offer: I’ll give you $10, and then we’ll toss the coin for $100.

No matter which way the coin comes up, you’ll be ahead $10 taking the second offer rather than the first. This means that the first choice is dominated by the second.

This doesn’t necessarily mean that you should go for the second offer. Depending on your circumstances (and whether you think I have some sort of trick coin), it may be sensible for you to reject both offers. But one thing is certain: it makes no sense to accept the first offer.

How does all this relate to index funds? If two companies both offer equity index funds based on the same index, then the funds should hold exactly the same stocks in the same proportions. The only difference between the two funds is how well their returns track the returns of the index.

The main reason for a fund lagging an index is its Management Expense Ratio (MER). If an index fund charges a 1% MER each year, then the fund must return 1% less to investors than the stocks produce.

Another contributor to index funds lagging their index is cash holdings. Funds vary in the amount of cash they keep around. Because stocks tend to give better returns than cash, over the long term, more cash means lower returns. Similar to this case is the possibility that the shares held by the index fund do not accurately mirror the index for whatever reason.

Another possibility is that the price of an index fund’s units does not accurately reflect the value of the underlying stocks. This is called a premium or a discount depending on whether the price is too high or too low.

Suppose that we have two index funds A and B that hold the proper mix of stocks, do not sell at a discount or premium, and hold very little cash. The only thing left to distinguish them is the MER. Fund A has a 0.2% MER, and fund B has a 1% MER.

This means that no matter what happens in the stock market, fund A will always give a 0.8% higher return than fund B. As an investing strategy, fund B is dominated by fund A. So why would anyone invest in fund B?

The only reasons I can see why anyone might invest in fund B come down to ignorance. Maybe fund B manages to market itself without focusing on the MER. Maybe people aren’t aware of fund A.

In theory, all index funds that track a particular index can be evaluated, and everyone should invest in the one that lags the index by the least. In practice, things don’t always work out this way.

Thursday, March 6, 2008

Most commentators advise people to reduce the percentage of stocks in their portfolios as they age. Some popular rules of thumb are to make the stock percentage 100 minus your age or 120 minus your age.

Larry Swedroe in his excellent book “Rational Investing in Irrational Times” offers his own advice. Swedroe expresses his advice in terms of how long until you need the money (time horizon) rather than age. (Canadian Capitalist also posted on this subject last month.)

Unlike almost everything else in his book, Swedroe offers this table with no analysis of where the numbers came from. I decided to try to come up with my own answer to this question.

It is surprisingly difficult to come up criteria for optimizing a portfolio for some end time. The best I have come up with so far is to optimize a portfolio for a particular target dollar amount. This is similar, but admittedly not exactly the same thing.

So, given a particular dollar amount you are trying to save up, what portfolio mix should you use to minimize the expected time before reaching this goal? Of course, the goal amount should grow with inflation so that you will end up with some fixed amount of purchasing power regardless of how long it takes.

I assumed you start with an initial investment without adding any more money along the way. I also assumed that you were limited to stocks, bonds, and risk-free short-term government debt with returns and volatility as compiled by John Norstad in this paper.

The results

Before letting my computer run for a couple of days to get the answer, I guessed that when you were far from your goal, the portfolio would be heavy with stocks and would start shifting money to bonds and risk-free investments as the goal came nearer.

When the results came in, my guess was more or less correct, but not in the way I expected. The optimal portfolio mix is 100% stocks until you get to 93% of the goal portfolio value. From 93% to 99.8% of the goal, stocks are smoothly shifted into risk-free investments. From 99.8% of the goal onwards, the portfolio is entirely risk-free investments.

At a few points the optimal portfolio had 5% bonds, but for the most part, bonds were completely absent.

Expressed in terms of time, the portfolio mix is 100% stocks until 18 months from the goal. Then stocks are sold steadily until the goal is two months away, and after that everything is in risk-free investments.

What does this mean?

Obviously the answer I came up with is radically different from Swedroe’s table. My table would look something like this:

I don’t recommend using this table. I don’t think you should have any money you will need within 3 years in stocks. A retired person should have at least 3 years worth of living expenses in fixed income investments. This gives you time for planning and adjusting to big upward or downward swings in the stock market.

However, I think it is likely that Swedroe’s table is too conservative. I would like to have seen how he came up with it.

Wednesday, March 5, 2008

There was an interesting discussion earlier this week over at Canadian Financial DIY about how much people should invest in stocks. This post pointed to an article by Zvi Bodie and Paul Hogan that discussed the cost of insuring a portfolio against loss among other things.

You may remember Bodie as a co-author of the book “Worry-Free Investing” (see my review of this book starting here). He is a big proponent of investing in inflation-protected bonds rather than stocks. His reasoning is basically that stocks are too risky, even though they are expected to give higher returns.

In their article, Bodie and Hogan make the following claim about insuring a portfolio: “proof positive of how stocks are risky even in the long run is that if you try to insure a portfolio against a shortfall, you will find that the premium rises as the time horizon lengthens.”

An Example

Let’s look at an example to explain what they mean. Suppose that you are about to invest $10,000 in a stock index, but are very worried about losing some of your money. You would like to pick a date in the future and buy insurance that tops up your stocks to $10,000 on that date if the stocks are worth less than $10,000. If they are worth more than $10,000, you get to keep the excess and the insurance pays nothing.

How much should this insurance cost? This depends on how far into the future you choose for the insurance top-up date. Bodie and Hogan claim that as you push this date further into the future, insurance costs rise.

Does this really make sense? I agree that insurance for a month will cost less than insurance for a year, but what about comparing 5 years and 30 years? It seems to me that there is much less risk of losing money over 30 years than over 5 years. This would make the 5-year insurance more expensive and would contradict Bodie and Hogan.

Some Analysis

I decided to do some figuring to test my hunch. I had to make some assumptions about stock returns. Suppose that the expected compound stock return is 7% per year with a 30% standard deviation (both of these figures are worse than historical US data).

Here are the results of what the insurance should cost for different lengths of time before the insurance top-up date:

As we can see from this chart, the insurance cost rises to a maximum after about 5 years, but then starts to drop. By this measure, after the first 5 years, owning stocks starts to become less risky. This casts doubt on Bodie’s arguments against owning stocks.

Tuesday, March 4, 2008

Researchers at the University of Cambridge have found simple ways to compromise bank card readers. The next time you’re at a store punching your PIN into a debit card reader, if there is a paperclip or needle sticking out the back of the reader, you should be suspicious.

The researchers Drimer, Murdoch, and Anderson have documented their findings in this technical report. They chose two different models of card reader and bought two each of them online for a total of $80 for the four readers. They then took one of each type apart to see how it worked and were then able to compromise the other readers simply.

The card readers they examined were actually a type that is intended to work with higher security bank cards called smart cards. Instead of just a magnetic stripe, these cards contain a microchip that gives higher security. These cards are being deployed throughout Europe and are currently being tested in Canada.

The researchers were able to probe the inside of the reader to get PINs and customer identities. This information makes it possible to make a duplicate bank card that can be used with the stolen PIN to clean out the victim’s bank account.

For one type of reader the researchers poked a paperclip through an existing hole in the back of the reader to access internal information. For the other type of reader, they had to drill a tiny hole and insert a needle. In both cases they then connected a wire to the paperclip or needle and ran the wire to a device to store PINs and customer identities.

The researchers also demonstrated their attack for television: “Having tested this attack in the laboratory, we repeated it in the field for the BBC ‘Newsnight’ programme; we tapped a terminal in a London shop and, during a transaction, extracted the card and PIN details for a journalist’s card without triggering the tamper detection system.”

Although these attacks were carried out against smart card readers, the problem has nothing to do with whether the bank card is a smart card or regular magnetic stripe card. The researchers were able to bypass security and read out important information from inside the card reader.

In North America customers are protected financially from attacks like this because they are usually not held liable. The results can be very distressing while the problem is being sorted out, but in the end customers rarely lose the stolen money.

According to the researchers, the situation is much different in the UK. They say that their results “will encourage improved security and better treatment of customers, who are often blamed for fraud.”

Monday, March 3, 2008

How you ever wondered what all the fuss is about with pension disputes? We often hear about battles between a company and its workers over pensions. The workers accuse the company of stealing from the pension fund, and the company denies it. The stories rarely make it clear what is going on.

In his usual clear and compelling way, Warren Buffett discusses pensions in his latest letter to shareholders on page 17 in a section called “Fanciful Figures – How Public Companies Juice Earnings.”

Why Should Pension Funds Exist at All?

Let’s consider the case of a 45-year old worker William who works for the fictitious company SomeCorp. A traditional pension is a promise made by SomeCorp to pay William certain amounts of money each month after he retires.

Given this situation, it’s not immediately clear why a pension fund should exist at all. As long as SomeCorp makes the promised payments, the company should be able to run its affairs as it sees fit, right? Not so fast. What happens if SomeCorp goes out of business?

If SomeCorp has not set aside any money to pay pensions or they spend all this money in a failed attempt to save the business, then all retired workers will stop receiving their pension money, and current workers will never get any of their promised pensions. This is definitely a bad situation.

So, there are laws requiring companies to set aside money in a pension fund to cover their pension obligations. Pension payments to William will come out of a pension fund.

How Much Money Should be in the Pension Fund?

If SomeCorp hires more workers, or something else changes that causes the total amount in the pension fund to be less than what is needed to cover future promised pension payments, then SomeCorp has to add more money to the fund. Other changes may reduce SomeCorp’s pension obligations allowing them to take money out of the fund.

But, how can we know that the pension fund holds the right amount of money? The truth is that we can’t tell for certain. SomeCorp has to guess what payments it will have to make, and it has to guess how well the investments in the pension fund will perform over time.

Potential Abuses

This creates the potential for abuses. If SomeCorp makes rosy projections, they will not have to put much money in the pension fund. It will take many years to prove that the projections are unrealistic, and by then the current management will be long gone. In the mean time, SomeCorp management can report higher earnings each year and collect bigger bonuses and stock option gains.

According to Buffett, this kind of abuse is widespread among public companies trying to report the highest profits they can even if those profits don’t reflect reality.

When management and workers disagree over how much money needs to be in the pension fund, the workers accuse management of “stealing from the pension fund.”

A Simple Example

Getting back to the 45-year old worker William, let’s assume that he has a very simple pension. He will get $2000 per month for 20 years starting at age 65. These payments are indexed to inflation (assumed to be 3%) so that William will have the purchasing power each month of 2000 of today’s dollars.

Given the mix of cash, bonds, and stocks in the pension fund, and the costs of managing the fund, suppose that a realistic guess of the long-term investment returns is 6.5% per year. Based on this assumption, we can calculate that SomeCorp needs to have $179,000 set aside in the pension fund to cover William’s payments.

What happens if SomeCorp assumes long-term returns will be 8% instead of 6.5%? Then they only have to put aside $120,000, a savings of $59,000. Of course, these savings aren’t real. If returns turn out to be only 6.5% per year, then this shortfall will have to be made up later or William won’t get his full pension.

If we multiply this $59,000 shortfall by the number of workers, the amounts become very large. If SomeCorp falls on hard times, it might not be able to make up this shortfall when it comes time to pay out the pensions.

If SomeCorp decided to increase its assumed pension fund investment returns to 8.1%, it could pull $3100 per worker out of the pension fund. You can see why workers would accuse SomeCorp of stealing from the pension fund if management played accounting games like this.